Subdivisions from primal and dual cones and polytopes
type: Item
instance of: scholarly article
title: Subdivisions from primal and dual cones and polytopes
zbMATH Open document ID: 0554.52012
DOI: 10.1016/0024-3795(84)90103-4
author: B. Curtis Eaves
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: Giving a convex polytope P which contains the origin of \({\mathbb{R}}^ n\) in its interior and its polar polytope \(P^*\) \((=\{y\in {\mathbb{R}}^ n:\quad xy\leq 1\quad for\quad allx\in P\}),\) there is a 1-1 correspondence between the faces of P and \(P^*\) \((F\leftrightarrow F^*=\{y\in P^*:\quad xy=1\quad for\quad all\quad x\in F\}).\) Using this correspondence a tiling of \({\mathbb{R}}^ n\times [0,+\infty]\) with finitely many convex polyhedral cones with apexes at the origin is constructed (depending on a parameter).
reviewed by: Peter M. Gruber
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 3883118
zbMATH Keywords: tiling with cones
zbMATH Keywords: polar polytope
zbMATH Keywords: convex polyhedral cones
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90103-4
OpenAlex ID: W2016634390
cites work: Q5547252
cites work: Q3845569
description: scientific article; zbMATH DE number 3883118